Explicit Maximally Recoverable Codes with Locality

TL;DR

This paper introduces explicit constructions of maximally-recoverable codes with locality, balancing local quick recovery and global erasure tolerance, and explores the trade-offs with alphabet size.

Contribution

It provides the first explicit families of maximally-recoverable codes with locality and studies the relationship between recoverability and alphabet size.

Findings

Explicit code constructions with maximal recoverability and locality.

Analysis of the trade-off between recoverability and alphabet size.

Foundations for future research on efficient erasure correction.

Abstract

Consider a systematic linear code where some (local) parity symbols depend on few prescribed symbols, while other (heavy) parity symbols may depend on all data symbols. Local parities allow to quickly recover any single symbol when it is erased, while heavy parities provide tolerance to a large number of simultaneous erasures. A code as above is maximally-recoverable if it corrects all erasure patterns which are information theoretically recoverable given the code topology. In this paper we present explicit families of maximally-recoverable codes with locality. We also initiate the study of the trade-off between maximal recoverability and alphabet size.